Put an oven rack in the center of the oven. Preheat the oven to 475 degrees F. Sprinkle a heavy baking sheet (without sides) with cornmeal and set aside.
In a large skillet, melt 3 tablespoons of olive oil and the butter over medium-low heat. Add the onions, salt and pepper. Cook, stirring occasionally, until golden and caramelized, about 20 minutes. Increase the heat to medium-high and add the sausage. Using a wooden spoon, break up the sausage and cook, stirring constantly, until cooked through, about 8 minutes. Set aside to cool slightly.
On a lightly floured work surface, roll out the dough into a 13-inch diameter circle, about 1/4-inch thick. Transfer the dough to the prepared baking sheet and drizzle with olive oil. Spread the onion mixture evenly over the dough, leaving a 1-inch border. Sprinkle the cheese on top. Bake until the crust is golden and the cheese has melted, about 15 to 17 minutes. Remove from the oven and sprinkle with chopped basil. Cut the pizza into wedges and serve.